TSTP Solution File: SET640+3 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET640+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 15:09:00 EDT 2024
% Result : Theorem 0.22s 0.45s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 15
% Syntax : Number of formulae : 77 ( 7 unt; 0 def)
% Number of atoms : 434 ( 0 equ)
% Maximal formula atoms : 12 ( 5 avg)
% Number of connectives : 621 ( 264 ~; 227 |; 78 &)
% ( 11 <=>; 41 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-2 aty)
% Number of variables : 140 ( 110 !; 30 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f904,plain,
$false,
inference(resolution,[],[f903,f100]) ).
fof(f100,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f19]) ).
fof(f19,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p19) ).
fof(f903,plain,
~ ilf_type(sK4,set_type),
inference(resolution,[],[f902,f100]) ).
fof(f902,plain,
( ~ ilf_type(sK5,set_type)
| ~ ilf_type(sK4,set_type) ),
inference(resolution,[],[f901,f100]) ).
fof(f901,plain,
( ~ ilf_type(sK6,set_type)
| ~ ilf_type(sK4,set_type)
| ~ ilf_type(sK5,set_type) ),
inference(resolution,[],[f900,f100]) ).
fof(f900,plain,
( ~ ilf_type(sK7,set_type)
| ~ ilf_type(sK4,set_type)
| ~ ilf_type(sK6,set_type)
| ~ ilf_type(sK5,set_type) ),
inference(resolution,[],[f899,f97]) ).
fof(f97,plain,
ilf_type(sK7,relation_type(sK5,sK6)),
inference(cnf_transformation,[],[f60]) ).
fof(f60,plain,
( ~ subset(sK4,cross_product(sK5,sK6))
& subset(sK4,sK7)
& ilf_type(sK7,relation_type(sK5,sK6))
& ilf_type(sK6,set_type)
& ilf_type(sK5,set_type)
& ilf_type(sK4,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7])],[f24,f59,f58,f57,f56]) ).
fof(f56,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ~ subset(X0,cross_product(X1,X2))
& subset(X0,X3)
& ilf_type(X3,relation_type(X1,X2)) )
& ilf_type(X2,set_type) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) )
=> ( ? [X1] :
( ? [X2] :
( ? [X3] :
( ~ subset(sK4,cross_product(X1,X2))
& subset(sK4,X3)
& ilf_type(X3,relation_type(X1,X2)) )
& ilf_type(X2,set_type) )
& ilf_type(X1,set_type) )
& ilf_type(sK4,set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f57,plain,
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ~ subset(sK4,cross_product(X1,X2))
& subset(sK4,X3)
& ilf_type(X3,relation_type(X1,X2)) )
& ilf_type(X2,set_type) )
& ilf_type(X1,set_type) )
=> ( ? [X2] :
( ? [X3] :
( ~ subset(sK4,cross_product(sK5,X2))
& subset(sK4,X3)
& ilf_type(X3,relation_type(sK5,X2)) )
& ilf_type(X2,set_type) )
& ilf_type(sK5,set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f58,plain,
( ? [X2] :
( ? [X3] :
( ~ subset(sK4,cross_product(sK5,X2))
& subset(sK4,X3)
& ilf_type(X3,relation_type(sK5,X2)) )
& ilf_type(X2,set_type) )
=> ( ? [X3] :
( ~ subset(sK4,cross_product(sK5,sK6))
& subset(sK4,X3)
& ilf_type(X3,relation_type(sK5,sK6)) )
& ilf_type(sK6,set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f59,plain,
( ? [X3] :
( ~ subset(sK4,cross_product(sK5,sK6))
& subset(sK4,X3)
& ilf_type(X3,relation_type(sK5,sK6)) )
=> ( ~ subset(sK4,cross_product(sK5,sK6))
& subset(sK4,sK7)
& ilf_type(sK7,relation_type(sK5,sK6)) ) ),
introduced(choice_axiom,[]) ).
fof(f24,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ~ subset(X0,cross_product(X1,X2))
& subset(X0,X3)
& ilf_type(X3,relation_type(X1,X2)) )
& ilf_type(X2,set_type) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) ),
inference(flattening,[],[f23]) ).
fof(f23,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ~ subset(X0,cross_product(X1,X2))
& subset(X0,X3)
& ilf_type(X3,relation_type(X1,X2)) )
& ilf_type(X2,set_type) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f21]) ).
fof(f21,negated_conjecture,
~ ! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X1,X2))
=> ( subset(X0,X3)
=> subset(X0,cross_product(X1,X2)) ) ) ) ) ),
inference(negated_conjecture,[],[f20]) ).
fof(f20,conjecture,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X1,X2))
=> ( subset(X0,X3)
=> subset(X0,cross_product(X1,X2)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_2) ).
fof(f899,plain,
( ~ ilf_type(sK7,relation_type(sK5,sK6))
| ~ ilf_type(sK4,set_type)
| ~ ilf_type(sK7,set_type)
| ~ ilf_type(sK6,set_type)
| ~ ilf_type(sK5,set_type) ),
inference(resolution,[],[f896,f100]) ).
fof(f896,plain,
( ~ ilf_type(cross_product(sK5,sK6),set_type)
| ~ ilf_type(sK7,set_type)
| ~ ilf_type(sK4,set_type)
| ~ ilf_type(sK7,relation_type(sK5,sK6))
| ~ ilf_type(sK6,set_type)
| ~ ilf_type(sK5,set_type) ),
inference(resolution,[],[f895,f119]) ).
fof(f119,plain,
! [X2,X0,X1] :
( ilf_type(X2,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f32]) ).
fof(f32,plain,
! [X0] :
( ! [X1] :
( ( ! [X2] :
( ilf_type(X2,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X2,relation_type(X0,X1)) )
& ! [X3] :
( ilf_type(X3,relation_type(X0,X1))
| ~ ilf_type(X3,subset_type(cross_product(X0,X1))) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f22]) ).
fof(f22,plain,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> ilf_type(X2,subset_type(cross_product(X0,X1))) )
& ! [X3] :
( ilf_type(X3,subset_type(cross_product(X0,X1)))
=> ilf_type(X3,relation_type(X0,X1)) ) ) ) ),
inference(rectify,[],[f4]) ).
fof(f4,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( ! [X3] :
( ilf_type(X3,relation_type(X0,X1))
=> ilf_type(X3,subset_type(cross_product(X0,X1))) )
& ! [X2] :
( ilf_type(X2,subset_type(cross_product(X0,X1)))
=> ilf_type(X2,relation_type(X0,X1)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p4) ).
fof(f895,plain,
( ~ ilf_type(sK7,subset_type(cross_product(sK5,sK6)))
| ~ ilf_type(cross_product(sK5,sK6),set_type)
| ~ ilf_type(sK7,set_type)
| ~ ilf_type(sK4,set_type) ),
inference(resolution,[],[f879,f100]) ).
fof(f879,plain,
( ~ ilf_type(power_set(cross_product(sK5,sK6)),set_type)
| ~ ilf_type(sK4,set_type)
| ~ ilf_type(cross_product(sK5,sK6),set_type)
| ~ ilf_type(sK7,set_type)
| ~ ilf_type(sK7,subset_type(cross_product(sK5,sK6))) ),
inference(duplicate_literal_removal,[],[f876]) ).
fof(f876,plain,
( ~ ilf_type(cross_product(sK5,sK6),set_type)
| ~ ilf_type(sK4,set_type)
| ~ ilf_type(power_set(cross_product(sK5,sK6)),set_type)
| ~ ilf_type(sK7,set_type)
| ~ ilf_type(sK7,subset_type(cross_product(sK5,sK6)))
| ~ ilf_type(sK7,set_type)
| ~ ilf_type(cross_product(sK5,sK6),set_type) ),
inference(resolution,[],[f875,f128]) ).
fof(f128,plain,
! [X0,X1] :
( ilf_type(X1,member_type(power_set(X0)))
| ~ ilf_type(X1,subset_type(X0))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f80]) ).
fof(f80,plain,
! [X0] :
( ! [X1] :
( ( ( ilf_type(X1,subset_type(X0))
| ~ ilf_type(X1,member_type(power_set(X0))) )
& ( ilf_type(X1,member_type(power_set(X0)))
| ~ ilf_type(X1,subset_type(X0)) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f37]) ).
fof(f37,plain,
! [X0] :
( ! [X1] :
( ( ilf_type(X1,subset_type(X0))
<=> ilf_type(X1,member_type(power_set(X0))) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( ilf_type(X1,subset_type(X0))
<=> ilf_type(X1,member_type(power_set(X0))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p8) ).
fof(f875,plain,
( ~ ilf_type(sK7,member_type(power_set(cross_product(sK5,sK6))))
| ~ ilf_type(cross_product(sK5,sK6),set_type)
| ~ ilf_type(sK4,set_type)
| ~ ilf_type(power_set(cross_product(sK5,sK6)),set_type)
| ~ ilf_type(sK7,set_type) ),
inference(resolution,[],[f874,f100]) ).
fof(f874,plain,
( ~ ilf_type(sK12(sK7,cross_product(sK5,sK6)),set_type)
| ~ ilf_type(sK4,set_type)
| ~ ilf_type(cross_product(sK5,sK6),set_type)
| ~ ilf_type(sK7,member_type(power_set(cross_product(sK5,sK6))))
| ~ ilf_type(power_set(cross_product(sK5,sK6)),set_type)
| ~ ilf_type(sK7,set_type) ),
inference(duplicate_literal_removal,[],[f871]) ).
fof(f871,plain,
( ~ ilf_type(sK4,set_type)
| ~ ilf_type(sK12(sK7,cross_product(sK5,sK6)),set_type)
| ~ ilf_type(cross_product(sK5,sK6),set_type)
| ~ ilf_type(sK7,member_type(power_set(cross_product(sK5,sK6))))
| ~ ilf_type(power_set(cross_product(sK5,sK6)),set_type)
| ~ ilf_type(sK7,set_type)
| ~ ilf_type(cross_product(sK5,sK6),set_type) ),
inference(resolution,[],[f698,f102]) ).
fof(f102,plain,
! [X0] :
( ~ empty(power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f26]) ).
fof(f26,plain,
! [X0] :
( ( ilf_type(power_set(X0),set_type)
& ~ empty(power_set(X0)) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f12]) ).
fof(f12,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ( ilf_type(power_set(X0),set_type)
& ~ empty(power_set(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p12) ).
fof(f698,plain,
( empty(power_set(cross_product(sK5,sK6)))
| ~ ilf_type(sK4,set_type)
| ~ ilf_type(sK12(sK7,cross_product(sK5,sK6)),set_type)
| ~ ilf_type(cross_product(sK5,sK6),set_type)
| ~ ilf_type(sK7,member_type(power_set(cross_product(sK5,sK6))))
| ~ ilf_type(power_set(cross_product(sK5,sK6)),set_type)
| ~ ilf_type(sK7,set_type) ),
inference(duplicate_literal_removal,[],[f697]) ).
fof(f697,plain,
( ~ ilf_type(sK7,set_type)
| ~ ilf_type(sK4,set_type)
| ~ ilf_type(sK12(sK7,cross_product(sK5,sK6)),set_type)
| ~ ilf_type(cross_product(sK5,sK6),set_type)
| ~ ilf_type(sK7,member_type(power_set(cross_product(sK5,sK6))))
| ~ ilf_type(power_set(cross_product(sK5,sK6)),set_type)
| empty(power_set(cross_product(sK5,sK6)))
| ~ ilf_type(sK7,set_type) ),
inference(resolution,[],[f690,f142]) ).
fof(f142,plain,
! [X0,X1] :
( member(X0,X1)
| ~ ilf_type(X0,member_type(X1))
| ~ ilf_type(X1,set_type)
| empty(X1)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f89]) ).
fof(f89,plain,
! [X0] :
( ! [X1] :
( ( ( ilf_type(X0,member_type(X1))
| ~ member(X0,X1) )
& ( member(X0,X1)
| ~ ilf_type(X0,member_type(X1)) ) )
| ~ ilf_type(X1,set_type)
| empty(X1) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f44]) ).
fof(f44,plain,
! [X0] :
( ! [X1] :
( ( ilf_type(X0,member_type(X1))
<=> member(X0,X1) )
| ~ ilf_type(X1,set_type)
| empty(X1) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f43]) ).
fof(f43,plain,
! [X0] :
( ! [X1] :
( ( ilf_type(X0,member_type(X1))
<=> member(X0,X1) )
| ~ ilf_type(X1,set_type)
| empty(X1) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f13]) ).
fof(f13,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ( ilf_type(X1,set_type)
& ~ empty(X1) )
=> ( ilf_type(X0,member_type(X1))
<=> member(X0,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p13) ).
fof(f690,plain,
( ~ member(sK7,power_set(cross_product(sK5,sK6)))
| ~ ilf_type(sK7,set_type)
| ~ ilf_type(sK4,set_type)
| ~ ilf_type(sK12(sK7,cross_product(sK5,sK6)),set_type)
| ~ ilf_type(cross_product(sK5,sK6),set_type) ),
inference(resolution,[],[f688,f98]) ).
fof(f98,plain,
subset(sK4,sK7),
inference(cnf_transformation,[],[f60]) ).
fof(f688,plain,
( ~ subset(sK4,sK7)
| ~ ilf_type(cross_product(sK5,sK6),set_type)
| ~ ilf_type(sK7,set_type)
| ~ ilf_type(sK4,set_type)
| ~ ilf_type(sK12(sK7,cross_product(sK5,sK6)),set_type)
| ~ member(sK7,power_set(cross_product(sK5,sK6))) ),
inference(duplicate_literal_removal,[],[f653]) ).
fof(f653,plain,
( ~ member(sK7,power_set(cross_product(sK5,sK6)))
| ~ ilf_type(cross_product(sK5,sK6),set_type)
| ~ ilf_type(sK7,set_type)
| ~ ilf_type(sK4,set_type)
| ~ ilf_type(sK12(sK7,cross_product(sK5,sK6)),set_type)
| ~ subset(sK4,sK7)
| ~ ilf_type(cross_product(sK5,sK6),set_type)
| ~ ilf_type(sK7,set_type)
| ~ ilf_type(sK4,set_type) ),
inference(resolution,[],[f651,f180]) ).
fof(f180,plain,
! [X0] :
( ~ subset(X0,cross_product(sK5,sK6))
| ~ subset(sK4,X0)
| ~ ilf_type(cross_product(sK5,sK6),set_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK4,set_type) ),
inference(resolution,[],[f130,f99]) ).
fof(f99,plain,
~ subset(sK4,cross_product(sK5,sK6)),
inference(cnf_transformation,[],[f60]) ).
fof(f130,plain,
! [X2,X0,X1] :
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f39]) ).
fof(f39,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1)
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f38]) ).
fof(f38,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1)
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( ( subset(X1,X2)
& subset(X0,X1) )
=> subset(X0,X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).
fof(f651,plain,
( subset(sK7,cross_product(sK5,sK6))
| ~ member(sK7,power_set(cross_product(sK5,sK6)))
| ~ ilf_type(cross_product(sK5,sK6),set_type)
| ~ ilf_type(sK7,set_type)
| ~ ilf_type(sK4,set_type)
| ~ ilf_type(sK12(sK7,cross_product(sK5,sK6)),set_type) ),
inference(duplicate_literal_removal,[],[f641]) ).
fof(f641,plain,
( ~ ilf_type(sK12(sK7,cross_product(sK5,sK6)),set_type)
| ~ member(sK7,power_set(cross_product(sK5,sK6)))
| ~ ilf_type(cross_product(sK5,sK6),set_type)
| ~ ilf_type(sK7,set_type)
| ~ ilf_type(sK7,set_type)
| ~ ilf_type(sK4,set_type)
| subset(sK7,cross_product(sK5,sK6))
| ~ ilf_type(cross_product(sK5,sK6),set_type)
| ~ ilf_type(sK7,set_type) ),
inference(resolution,[],[f299,f122]) ).
fof(f122,plain,
! [X0,X1] :
( member(sK12(X0,X1),X0)
| subset(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f75]) ).
fof(f75,plain,
! [X0] :
( ! [X1] :
( ( ( subset(X0,X1)
| ( ~ member(sK12(X0,X1),X1)
& member(sK12(X0,X1),X0)
& ilf_type(sK12(X0,X1),set_type) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ ilf_type(X3,set_type) )
| ~ subset(X0,X1) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f73,f74]) ).
fof(f74,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X1)
& member(X2,X0)
& ilf_type(X2,set_type) )
=> ( ~ member(sK12(X0,X1),X1)
& member(sK12(X0,X1),X0)
& ilf_type(sK12(X0,X1),set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f73,plain,
! [X0] :
( ! [X1] :
( ( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0)
& ilf_type(X2,set_type) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ ilf_type(X3,set_type) )
| ~ subset(X0,X1) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(rectify,[],[f72]) ).
fof(f72,plain,
! [X0] :
( ! [X1] :
( ( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0)
& ilf_type(X2,set_type) ) )
& ( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type) )
| ~ subset(X0,X1) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f34]) ).
fof(f34,plain,
! [X0] :
( ! [X1] :
( ( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f33]) ).
fof(f33,plain,
! [X0] :
( ! [X1] :
( ( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( subset(X0,X1)
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ( member(X2,X0)
=> member(X2,X1) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p6) ).
fof(f299,plain,
! [X0] :
( ~ member(sK12(sK7,cross_product(sK5,sK6)),X0)
| ~ ilf_type(sK12(sK7,cross_product(sK5,sK6)),set_type)
| ~ member(X0,power_set(cross_product(sK5,sK6)))
| ~ ilf_type(cross_product(sK5,sK6),set_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK7,set_type)
| ~ ilf_type(sK4,set_type) ),
inference(duplicate_literal_removal,[],[f292]) ).
fof(f292,plain,
! [X0] :
( ~ member(sK12(sK7,cross_product(sK5,sK6)),X0)
| ~ ilf_type(sK12(sK7,cross_product(sK5,sK6)),set_type)
| ~ member(X0,power_set(cross_product(sK5,sK6)))
| ~ ilf_type(cross_product(sK5,sK6),set_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK7,set_type)
| ~ ilf_type(sK4,set_type)
| ~ ilf_type(cross_product(sK5,sK6),set_type) ),
inference(resolution,[],[f124,f189]) ).
fof(f189,plain,
( ~ member(sK12(sK7,cross_product(sK5,sK6)),cross_product(sK5,sK6))
| ~ ilf_type(sK7,set_type)
| ~ ilf_type(sK4,set_type)
| ~ ilf_type(cross_product(sK5,sK6),set_type) ),
inference(resolution,[],[f186,f98]) ).
fof(f186,plain,
! [X0] :
( ~ subset(sK4,X0)
| ~ ilf_type(cross_product(sK5,sK6),set_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK4,set_type)
| ~ member(sK12(X0,cross_product(sK5,sK6)),cross_product(sK5,sK6)) ),
inference(duplicate_literal_removal,[],[f185]) ).
fof(f185,plain,
! [X0] :
( ~ subset(sK4,X0)
| ~ ilf_type(cross_product(sK5,sK6),set_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK4,set_type)
| ~ member(sK12(X0,cross_product(sK5,sK6)),cross_product(sK5,sK6))
| ~ ilf_type(cross_product(sK5,sK6),set_type)
| ~ ilf_type(X0,set_type) ),
inference(resolution,[],[f180,f123]) ).
fof(f123,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sK12(X0,X1),X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f75]) ).
fof(f124,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ ilf_type(X3,set_type)
| ~ member(X0,power_set(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f79]) ).
fof(f79,plain,
! [X0] :
( ! [X1] :
( ( ( member(X0,power_set(X1))
| ( ~ member(sK13(X0,X1),X1)
& member(sK13(X0,X1),X0)
& ilf_type(sK13(X0,X1),set_type) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ ilf_type(X3,set_type) )
| ~ member(X0,power_set(X1)) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f77,f78]) ).
fof(f78,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X1)
& member(X2,X0)
& ilf_type(X2,set_type) )
=> ( ~ member(sK13(X0,X1),X1)
& member(sK13(X0,X1),X0)
& ilf_type(sK13(X0,X1),set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f77,plain,
! [X0] :
( ! [X1] :
( ( ( member(X0,power_set(X1))
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0)
& ilf_type(X2,set_type) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ ilf_type(X3,set_type) )
| ~ member(X0,power_set(X1)) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(rectify,[],[f76]) ).
fof(f76,plain,
! [X0] :
( ! [X1] :
( ( ( member(X0,power_set(X1))
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0)
& ilf_type(X2,set_type) ) )
& ( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type) )
| ~ member(X0,power_set(X1)) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f36]) ).
fof(f36,plain,
! [X0] :
( ! [X1] :
( ( member(X0,power_set(X1))
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f35]) ).
fof(f35,plain,
! [X0] :
( ! [X1] :
( ( member(X0,power_set(X1))
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f11]) ).
fof(f11,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( member(X0,power_set(X1))
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ( member(X2,X0)
=> member(X2,X1) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p11) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.16 % Problem : SET640+3 : TPTP v8.1.2. Released v2.2.0.
% 0.13/0.18 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.40 % Computer : n022.cluster.edu
% 0.15/0.40 % Model : x86_64 x86_64
% 0.15/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.40 % Memory : 8042.1875MB
% 0.15/0.40 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.40 % CPULimit : 300
% 0.15/0.40 % WCLimit : 300
% 0.15/0.40 % DateTime : Tue Apr 30 01:07:15 EDT 2024
% 0.15/0.40 % CPUTime :
% 0.15/0.41 % (32767)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.42 % (307)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.15/0.42 % (304)WARNING: value z3 for option sas not known
% 0.15/0.42 % (303)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.42 % (305)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.42 % (304)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.15/0.42 % (302)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.42 % (306)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.15/0.42 % (308)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.22/0.43 TRYING [1]
% 0.22/0.43 TRYING [2]
% 0.22/0.44 TRYING [3]
% 0.22/0.44 TRYING [1]
% 0.22/0.44 TRYING [2]
% 0.22/0.45 % (307)First to succeed.
% 0.22/0.45 TRYING [4]
% 0.22/0.45 % (307)Refutation found. Thanks to Tanya!
% 0.22/0.45 % SZS status Theorem for theBenchmark
% 0.22/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.45 % (307)------------------------------
% 0.22/0.45 % (307)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.22/0.45 % (307)Termination reason: Refutation
% 0.22/0.45
% 0.22/0.45 % (307)Memory used [KB]: 1520
% 0.22/0.45 % (307)Time elapsed: 0.036 s
% 0.22/0.45 % (307)Instructions burned: 129 (million)
% 0.22/0.45 % (307)------------------------------
% 0.22/0.45 % (307)------------------------------
% 0.22/0.45 % (32767)Success in time 0.045 s
%------------------------------------------------------------------------------